1. Field of the Invention
The present invention relates to methods for interpolating seismic data wherein such methods account for spatially aliased events. Interpolation of spatially aliased events enables the generation of high resolution data in preparation for various multi-trace process and in particular for migration.
2. Description of the Prior Art
For many multi-trace seismic processing methods fine resolution digital data are required. Migration processing is an example of a multi-trace seismic process requiring such highly resolved digital data. In order to achieve sufficient resolution, seismic receivers, such as geophones, are generally spaced apart so as to achieve a sampling interval from between about 5 to about 25 meters. In some instances, the sampling interval can be as fine as 1 meter.
However, poor seismic processing results can be obtained when the sample interval selected is too large. For example, FIG. 1, is a schematic cross section of a geological formation A illustrating a plurality of seismic traces B recorded by discrete geophones (not shown). The geophones are spaced at sampling interval C. Each seismic trace B includes a plurality of reflection events D thereon. Ideally, each reflection event D correspond to a discrete interface E between geological strata. Upon continued analysis and processing of the seismic traces B, the geological dip or slope of the imaged formation might appear to proceed along line F--F and not along line G--G. Line G--G represents the true slope or dip of the geological formation D. The apparent slope of the geological formation D represented by line F--F results from spatially aliased seismic traces.
The occurrence of spatial aliasing between seismic traces is related to the sampling interval of the seismic receiver. In other words, tighter sampling intervals between seismic sensors produce greater resolution of steep sloping geological formations.
FIG. 2 illustrates the same geological formations with a tighter or finer sampling interval (1/4 C). Here, the true geological slope represented by line G--G is clearly apparent.
However, collecting data on a fine sampling interval in the field significantly adds to the cost of seismic data acquisition particularly in the case of three dimensional (3D) surveying. Some benefit can be obtained by interpolating coarsely sampled seismic data and more particularly, coarsely sampled spatially aliased seismic data.
In general, interpolation can be described as the determination of values at locations from near by values, wherein such determined values have not been measured or specified. In the case of coarsely sampled seismic traces, interpolation provides an unmeasured value, preferably a value consistent with a reflection event, between measured reflection event recorded by discrete seismic sensors. In this way, interpolation may reduce the cost of data acquisition by permitting larger sampling intervals yet providing data suitably formatted (data appearing to be sampled at finer intervals) for improved multi-trace processing. However, when the spacial aliasing occurs in seismic data, present interpolation techniques do not significantly improve the seismic processing result. The effect of multi-trace processing of spatially aliased seismic traces is illustrated in the article "Trace Interpolation In Seismic Data Processing" (V. Bardan, Geophysical Prospecting, 35, pp 343-358, 1987). In this article, migration of spatially aliased traces produces very poor results.
A number of interpolation techniques are available. The simplest of these is sinc interpolation. However this technique is ineffective on spatially aliased traces. Another technique (J. J. Raoult, Expanded Abstracts, SEG Convention, Atlanta, 1984, pp 761-763) searches multi-trace data in the t-x domain for the locally most coherent one or two dips, and interpolates amplitudes along the dip directions. The limitation of this method is that it only interpolates data on a line by line basis, typically the cross-line direction in a 3D survey. The ideal interpolation would use all of the data in the vicinity of the region being interpolated.